Diketahui f(x) = 3x-6 dan g(x) = 2x+a. Bila (fog)(x) = (gof)(x), maka nilai a adalah

Bab Fungsi Komposisi
Matematika SMA Kelas X

(fog) (x) = (gof) (x)
f(2x + a) = g(3x - 6)
3(2x + a) - 6 = 2(3x - 6) + a
6x + 3a - 6 = 6x - 12 + a
◎◎ coret 6x ◎◎

3a - a = - 12 + 6
2a = -6
a = -3

(fog)(x) = (gof)(x)
f(g(x)) = g(f(x))
3(2x+a)-6 = 2(3x-6)+a
6x + 3a - 6 = 6x - 12 + a
= 6x - 12 + a - 6x - 3a + 6
= -6 - 2a
2a = -6
a = -6/2
a = -3